Optimal. Leaf size=9 \[ \log \left (\frac {\log (x)}{x}+1\right ) \]
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Rubi [A] time = 0.07, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6712, 31} \[ \log \left (\frac {\log (x)}{x}+1\right ) \]
Antiderivative was successfully verified.
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Rule 31
Rule 6712
Rubi steps
\begin {align*} \int \frac {1-\log (x)}{x (x+\log (x))} \, dx &=\operatorname {Subst}\left (\int \frac {1}{1+x} \, dx,x,\frac {\log (x)}{x}\right )\\ &=\log \left (1+\frac {\log (x)}{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.05, size = 10, normalized size = 1.11 \[ \log (x+\log (x))-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 10, normalized size = 1.11 \[ \log \left (x + \log \relax (x)\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 1.56 \[ -\log \relax (x) + \log \left (-x - \log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 11, normalized size = 1.22 \[ -\ln \relax (x )+\ln \left (x +\ln \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 10, normalized size = 1.11 \[ \log \left (x + \log \relax (x)\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 10, normalized size = 1.11 \[ \ln \left (x+\ln \relax (x)\right )-\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 8, normalized size = 0.89 \[ - \log {\relax (x )} + \log {\left (x + \log {\relax (x )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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